Efficient and well-balanced numerical methods for nonhydrostatic three-dimensional shallow flows with moving beds and boundaries

具有移动床和边界的非静水三维浅流的高效且平衡的数值方法

• 批准号: RGPIN-2020-06278
• 负责人: Mohammadian, Majid
• 金额: $ 4.29万
• 依托单位: University of Ottawa
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=717822
• 关键词: Efficient; well; balanced; numerical; methods

Many coastal and riverine problems such as erosion around hydraulic structures involve sharp gradients, free-surface flows, moving boundaries, nonhydrostatic pressure, rapid erosion/sedimentation, and in some cases, supercritical flows. The efficient and accurate simulation of such problems can tremendously improve the design, maintenance, and management of hydraulic infrastructures. Furthermore, with the increasing availability and progress of computing systems and cloud computing facilities, there is a substantial need for improved computational schemes specific to hydro-environmental problems that are optimized for computers with parallel processing capability and can solve problems with complex flow regimes and moving beds and boundaries. The objective of this research program is to enhance the accuracy and performance of computational schemes for fully coupled simulation of 3D non-hydrostatic flow and sediment transport with moving beds and boundaries. The research program comprises two axes: the development of enhanced temporal integration schemes, and the development of spatial discretization methods specifically designed for coastal and riverine applications where the horizontal scales are typically larger than the vertical scales. To this end, novel optimized numerical schemes with high levels of accuracy and efficiency will be developed with particular emphasis on efficiency and stability for large time steps and large domains, as well as the capability of implementation on computers with parallel processing capacity. In these schemes, the sediment transport equations and the flow equations will be solved in a fully coupled form, and the model will be able to simulate complex flow regimes such as mixed sub/super/trans-critical flows. An important feature of the proposed numerical model is the ability to perform coupled 2D/3D simulations, which will make it applicable and efficient for a wide range of engineering problems involving sharp surface gradients, rapid erosion/sedimentation, and moving boundaries. The methodology proposed in this research can be applied in a number of practical problems, including fast-scour problems such as those induced by severe storm surges or tsunami-induced erosion around structures, scouring around bridge piers caused by flash floods, tailing-dam breaching, etc. Other applications include early warning systems and real-time simulations of field and lab cases where the speed and efficiency of the model plays a crucial role. Moreover, these advanced modeling tools can help a wide range of users, including designers, numerical modelers, and decision-makers in risk management applications and in the design and maintenance of hydraulic infrastructure in order to deal with the increased intensity of extreme precipitation, flooding, and storm surges, which typically lead to rapid erosion and sedimentation.

许多沿海和河流问题，如水工建筑物周围的侵蚀，涉及陡峭的坡度、自由面水流、移动边界、非静水压力、快速侵蚀/沉积，在某些情况下，还涉及超临界水流。对这类问题进行高效、准确的模拟，可以极大地改进水利基础设施的设计、维护和管理。此外，随着计算系统和云计算设施的可用性和进步，迫切需要针对水环境问题的改进计算方案，这些方案针对具有并行处理能力的计算机进行优化，可以解决复杂流型和移动床层和边界的问题。 本研究的目的是提高具有动床和边界的三维非静力水流和泥沙运动全耦合计算格式的精度和性能。该研究计划包括两个轴心：开发增强的时间综合方案，以及开发专门为水平尺度通常大于垂直尺度的沿海和河流应用而设计的空间离散方法。为此，将开发新的高精度和高效率的优化数值格式，特别强调大时间步长和大区域的效率和稳定性，以及在具有并行处理能力的计算机上执行的能力。在这些格式中，泥沙运动方程和水流方程将以完全耦合的形式进行求解，该模型将能够模拟复杂的流态，如亚/超/跨临界混合流动。 所提出的数值模型的一个重要特征是能够进行2D/3D耦合模拟，这将使其适用于广泛的工程问题，包括陡峭的表面梯度、快速的侵蚀/沉积和移动的边界。这项研究中提出的方法可以应用于许多实际问题，包括由强烈风暴潮或海啸引起的建筑物周围侵蚀引起的快速冲刷问题，由山洪暴发引起的桥墩冲刷问题，尾矿坝溃决等。其他应用包括预警系统和现场和实验室案例的实时模拟，模型的速度和效率起着至关重要的作用。此外，这些高级建模工具可以帮助广泛的用户，包括设计人员、数值建模人员和决策者，在风险管理应用程序以及水利基础设施的设计和维护方面，以应对极端降雨、洪水和风暴潮强度的增加，这些极端降雨、洪水和风暴潮通常会导致快速侵蚀和沉积。